Accreted stellar populations are comprised of the remnants of destroyed galaxies, and often dominate the 'stellar haloes' of galaxies such as the Milky Way (MW). This ensemble of external contributors is a key indicator of the past assembly history of a galaxy. We introduce a novel statistical method that uses the unbinned metallicity distribution function (MDF) of a stellar population to estimate the mass spectrum of its progenitors. Our model makes use of the well-known mass-metallicity relation of galaxies and assumes Gaussian MDF distributions for individual progenitors: the overall MDF is thus a mixture of MDFs from smaller galaxies. We apply the method to the stellar halo of the MW, as well as the classical MW satellite galaxies. The stellar components of the satellite galaxies have relatively small sample sizes, but we do not find any evidence for accreted populations with L > Lhost/100. We find that the MW stellar halo has N ~ 1-3 massive progenitors (L ≳ 108L⊙) within 10 kpc, and likely several hundred progenitors in total. We also test our method on simulations of MW-mass haloes, and find that our method is able to recover the true accreted population within a factor of 2. Future data sets will provide MDFs with orders of magnitude more stars, and this method could be a powerful technique to quantify the accreted populations down to the ultra-faint dwarf mass scale for both the MW and its satellites.